Abstract
We look for optimal quantum rotosensors, i.e., quantum spin states that are optimal in detecting rotations by a given angle. The exact quantity to be minimized is the probability that the rotated state projects onto the original one, averaged uniformly over all rotation axes. We show analytically that, for small rotation angles, the solution is given by anticoherent states. Numerical analysis shows that, for spin and , there exists, in each case, a critical rotation angle beyond which the minimum is instead achieved by the coherent states, the transition between the two being discontinuous. For , a third degenerate minimum appears in between the above two, consisting of pairs of antipodal points, regardless of the angle between their axes. We also determine the worst rotosensors, i.e., those states that maximize the above quantity; interestingly, the same set of states shows up but for different ranges of the rotation angle.
- Received 26 September 2016
DOI:https://doi.org/10.1103/PhysRevA.95.052125
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